Dynamics of a stochastic spatially extended system predicted by comparing deterministic and stochastic attractors of the corresponding birth-death process.
Dynamics of a stochastic spatially extended system predicted by comparing deterministic and stochastic attractors of the corresponding birth-death process.
复制标题
通过比较相应生灭过程的确定性吸引子和随机吸引子来预测随机空间扩展系统的动力学。
DOI：
10.1088/1478-3975/9/5/055002
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发表时间：
2012
期刊：
影响因子：
2
通讯作者：
Lipniacki,Tomasz
中科院分区：
文献类型：
--
作者：
Zuk,PawelJ;Kochańczyk,Marek;Jaruszewicz,Joanna;Bednorz,Witold;Lipniacki,Tomasz
活细胞可以看作是具有多稳态的生化反应器。这些状态之间的转换是由噪声实现的，或者在空间扩展的系统中，可能由于行波传播而发生。利用势场和温度场分析了一维随机生灭过程。势由过程的确定性极限定义，而温度场由噪声支配。稳定的稳态，其中潜在的有其全球最小值定义的全球确定性吸引子。对于随机系统，在低噪声限制，固定的概率分布成为单峰，集中在两个稳定的稳态，在这项研究中定义为全球随机吸引子。有趣的是，这两个吸引子可能位于不同的稳态。这一观察表明，空间扩展的随机系统的渐近行为取决于基板的扩散率和反应器的大小。我们证实了这一假设内的动力学蒙特卡罗模拟的六方晶格上的反应扩散模型。特别是，我们发现，虽然激酶-磷酸酶系统在一个小的域中保持不活动，激活行波可以传播时，一个更大的域被认为是。
Living cells may be considered as biochemical reactors of multiple steady states. Transitions between these states are enabled by noise, or, in spatially extended systems, may occur due to the traveling wave propagation. We analyze a one-dimensional bistable stochastic birth–death process by means of potential and temperature fields. The potential is defined by the deterministic limit of the process, while the temperature field is governed by noise. The stable steady state in which the potential has its global minimum defines the global deterministic attractor. For the stochastic system, in the low noise limit, the stationary probability distribution becomes unimodal, concentrated in one of two stable steady states, defined in this study as the global stochastic attractor. Interestingly, these two attractors may be located in different steady states. This observation suggests that the asymptotic behavior of spatially extended stochastic systems depends on the substrate diffusivity and size of the reactor. We confirmed this hypothesis within kinetic Monte Carlo simulations of a bistable reaction–diffusion model on the hexagonal lattice. In particular, we found that although the kinase–phosphatase system remains inactive in a small domain, the activatory traveling wave may propagate when a larger domain is considered.